Actually, using "they" to refer to a single subject is incorrect grammar. Using "he or she" or "he/she" is the correct way to refer to the cat.
Source: My Junior year English teacher would berate students who made this mistake ALL. THE. TIME.
English doesn't have singular non-gender specific pronouns so plural non-gender specific pronouns are correct to use. Read the article from white stag's song for more info.
...WHERE WERE YOU GUYS DURING MY HIGH SCHOOL JUNIOR YEAR ENGLISH CLASS??? I could've used this information! Meh, I guess I deserve it for just taking my teacher's word for it without exploring for myself. Sorry for the incorrect "correction," wiliaso. Thanks, guys.
Source: My Junior year English teacher would berate students who made this mistake ALL. THE. TIME.
http://motivatedgrammar.wordpress.com/2009/09/10/singular-they-and-the-many-reasons-why-its-correct/